5 research outputs found
Quantum Diffeomorphisms and Conformal Symmetry
We analyze the constraints of general coordinate invariance for quantum
theories possessing conformal symmetry in four dimensions. The character of
these constraints simplifies enormously on the Einstein universe . The global conformal symmetry algebra of this space determines
uniquely a finite shift in the Hamiltonian constraint from its classical value.
In other words, the global Wheeler-De Witt equation is {\it modified} at the
quantum level in a well-defined way in this case. We argue that the higher
moments of should not be imposed on the physical states {\it a priori}
either, but only the weaker condition . We
present an explicit example of the quantization and diffeomorphism constraints
on for a free conformal scalar field.Comment: PlainTeX File, 37 page
Conformal Invariance and Cosmic Background Radiation
The spectrum and statistics of the cosmic microwave background radiation
(CMBR) are investigated under the hypothesis that scale invariance of the
primordial density fluctuations should be promoted to full conformal
invariance. As in the theory of critical phenomena, this hypothesis leads in
general to deviations from naive scaling. The spectral index of the two-point
function of density fluctuations is given in terms of the quantum trace anomaly
and is greater than one, leading to less power at large distance scales than a
strict Harrison-Zel'dovich spectrum. Conformal invariance also implies
non-gaussian statistics for the higher point correlations and in particular, it
completely determines the large angular dependence of the three-point
correlations of the CMBR.Comment: 4 pages, Revtex file, uuencoded with one figur
Conformal invariance: from Weyl to SO(2,d)
The present work deals with two different but subtilely related kinds of
conformal mappings: Weyl rescaling in dimensional spaces and SO(2,d)
transformations. We express how the difference between the two can be
compensated by diffeomorphic transformations. This is well known in the
framework of String Theory but in the particular case of spaces. Indeed,
the Polyakov formalism describes world-sheets in terms of two-dimensional
conformal field theory. On the other hand, B. Zumino had shown that a classical
four-dimensional Weyl-invariant field theory restricted to live in Minkowski
space leads to an SO(2,4)-invariant field theory. We extend Zumino's result to
relate Weyl and SO(2,d) symmetries in arbitrary conformally flat spaces (CFS).
This allows us to assert that a classical -invariant field does not
distinguish, at least locally, between two different -dimensional CFSs.Comment: 5 pages, no figures. There are slight modifications to match with the
published versio
Cosmological Dark Energy: Prospects for a Dynamical Theory
We present an approach to the problem of vacuum energy in cosmology, based on
dynamical screening of Lambda on the horizon scale. We review first the
physical basis of vacuum energy as a phenomenon connected with macroscopic
boundary conditions, and the origin of the idea of its screening by particle
creation and vacuum polarization effects. We discuss next the relevance of the
quantum trace anomaly to this issue. The trace anomaly implies additional terms
in the low energy effective theory of gravity, which amounts to a non-trivial
modification of the classical Einstein theory, fully consistent with the
Equivalence Principle. We show that the new dynamical degrees of freedom the
anomaly contains provide a natural mechanism for relaxing Lambda to zero on
cosmological scales. We consider possible signatures of the restoration of
conformal invariance predicted by the fluctuations of these new scalar degrees
of freedom on the spectrum and statistics of the CMB, in light of the latest
bounds from WMAP. Finally we assess the prospects for a new cosmological model
in which the dark energy adjusts itself dynamically to the cosmological horizon
boundary, and therefore remains naturally of order H^2 at all times without
fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue
on Dark Energ
Conformal Invariance, Dark Energy, and CMB Non-Gaussianity
In addition to simple scale invariance, a universe dominated by dark energy
naturally gives rise to correlation functions possessing full conformal
invariance. This is due to the mathematical isomorphism between the conformal
group of certain 3 dimensional slices of de Sitter space and the de Sitter
isometry group SO(4,1). In the standard homogeneous isotropic cosmological
model in which primordial density perturbations are generated during a long
vacuum energy dominated de Sitter phase, the embedding of flat spatial sections
in de Sitter space induces a conformal invariant perturbation spectrum and
definite prediction for the shape of the non-Gaussian CMB bispectrum. In the
case in which the density fluctuations are generated instead on the de Sitter
horizon, conformal invariance of the horizon embedding implies a different but
also quite definite prediction for the angular correlations of CMB
non-Gaussianity on the sky. Each of these forms for the bispectrum is intrinsic
to the symmetries of de Sitter space and in that sense, independent of specific
model assumptions. Each is different from the predictions of single field slow
roll inflation models which rely on the breaking of de Sitter invariance. We
propose a quantum origin for the CMB fluctuations in the scalar gravitational
sector from the conformal anomaly that could give rise to these
non-Gaussianities without a slow roll inflaton field, and argue that conformal
invariance also leads to the expectation for the relation n_S-1=n_T between the
spectral indices of the scalar and tensor power spectrum. Confirmation of this
prediction or detection of non-Gaussian correlations in the CMB of one of the
bispectral shape functions predicted by conformal invariance can be used both
to establish the physical origins of primordial density fluctuations and
distinguish between different dynamical models of cosmological vacuum dark
energy.Comment: 73 pages, 9 figures. Final Version published in JCAP. New Section 4
added on linearized scalar gravitational potentials; New Section 8 added on
gravitational wave tensor perturbations and relation of spectral indices n_T
= n_S -1; Table of Contents added; Eqs. (3.14) and (3.15) added to clarify
relationship of bispectrum plotted to CMB measurements; Some other minor
modification